Model-Agnostic Meta-Learning (MAML) is one of the most successful meta-learning techniques for few-shot learning. It uses gradient descent to learn commonalities between various tasks, enabling the model to learn the meta-initialization of its own parameters to quickly adapt to new tasks using a small amount of labeled training data. A key challenge to few-shot learning is task uncertainty. Although a strong prior can be obtained from meta-learning with a large number of tasks, a precision model of the new task cannot be guaranteed because the volume of the training dataset is normally too small. In this study, first, in the process of choosing initialization parameters, the new method is proposed for task-specific learner adaptively learn to select initialization parameters that minimize the loss of new tasks. Then, we propose two improved methods for the meta-loss part: Method 1 generates weights by comparing meta-loss differences to improve the accuracy when there are few classes, and Method 2 introduces the homoscedastic uncertainty of each task to weigh multiple losses based on the original gradient descent, as a way to enhance the generalization ability to novel classes while ensuring accuracy improvement. Compared with previous gradient-based meta-learning methods, our model achieves better performance in regression tasks and few-shot classification and improves the robustness of the model to the learning rate and query sets in the meta-test set.

This paper introduces the notion of ``Initial Alignment'' (INAL) between a neural network at initialization and a target function. It is proved that if a network and a Boolean target function do not have a noticeable INAL, then noisy gradient descent on a fully connected network with normalized i.i.d. initialization will not learn in polynomial time. Thus a certain amount of knowledge about the target (measured by the INAL) is needed in the architecture design. This also provides an answer to an open problem posed in [AS20]. The results are based on deriving lower-bounds for descent algorithms on symmetric neural networks without explicit knowledge of the target function beyond its INAL.

In this paper, we revisit the online non-monotone continuous DR-submodular maximization problem over a down-closed convex set, which finds wide real-world applications in the domain of machine learning, economics, and operations research. At first, we present the Meta-MFW algorithm achieving a $1/e$-regret of $O(\sqrt{T})$ at the cost of $T^{3/2}$ stochastic gradient evaluations per round. As far as we know, Meta-MFW is the first algorithm to obtain $1/e$-regret of $O(\sqrt{T})$ for the online non-monotone continuous DR-submodular maximization problem over a down-closed convex set. Furthermore, in sharp contrast with ODC algorithm \citep{thang2021online}, Meta-MFW relies on the simple online linear oracle without discretization, lifting, or rounding operations. Considering the practical restrictions, we then propose the Mono-MFW algorithm, which reduces the per-function stochastic gradient evaluations from $T^{3/2}$ to 1 and achieves a $1/e$-regret bound of $O(T^{4/5})$. Next, we extend Mono-MFW to the bandit setting and propose the Bandit-MFW algorithm which attains a $1/e$-regret bound of $O(T^{8/9})$. To the best of our knowledge, Mono-MFW and Bandit-MFW are the first sublinear-regret algorithms to explore the one-shot and bandit setting for online non-monotone continuous DR-submodular maximization problem over a down-closed convex set, respectively. Finally, we conduct numerical experiments on both synthetic and real-world datasets to verify the effectiveness of our methods.

Malware is a major threat to computer systems and imposes many challenges to cyber security. Targeted threats, such as ransomware, cause millions of dollars in losses every year. The constant increase of malware infections has been motivating popular antiviruses (AVs) to develop dedicated detection strategies, which include meticulously crafted machine learning (ML) pipelines. However, malware developers unceasingly change their samples' features to bypass detection. This constant evolution of malware samples causes changes to the data distribution (i.e., concept drifts) that directly affect ML model detection rates, something not considered in the majority of the literature work. In this work, we evaluate the impact of concept drift on malware classifiers for two Android datasets: DREBIN (about 130K apps) and a subset of AndroZoo (about 285K apps). We used these datasets to train an Adaptive Random Forest (ARF) classifier, as well as a Stochastic Gradient Descent (SGD) classifier. We also ordered all datasets samples using their VirusTotal submission timestamp and then extracted features from their textual attributes using two algorithms (Word2Vec and TF-IDF). Then, we conducted experiments comparing both feature extractors, classifiers, as well as four drift detectors (DDM, EDDM, ADWIN, and KSWIN) to determine the best approach for real environments. Finally, we compare some possible approaches to mitigate concept drift and propose a novel data stream pipeline that updates both the classifier and the feature extractor. To do so, we conducted a longitudinal evaluation by (i) classifying malware samples collected over nine years (2009-2018), (ii) reviewing concept drift detection algorithms to attest its pervasiveness, (iii) comparing distinct ML approaches to mitigate the issue, and (iv) proposing an ML data stream pipeline that outperformed literature approaches.

The heart of Quantum Federated Learning (QFL) is associated with a distributed learning architecture across several local quantum devices and a more efficient training algorithm for the QFL is expected to minimize the communication overhead among different quantum participants. In this work, we put forth an efficient learning algorithm, namely federated quantum natural gradient descent (FQNGD), applied in a QFL framework which consists of the variational quantum circuit (VQC)-based quantum neural networks (QNN). The FQNGD algorithm admits much fewer training iterations for the QFL model to get converged and it can significantly reduce the total communication cost among local quantum devices. Compared with other federated learning algorithms, our experiments on a handwritten digit classification dataset corroborate the effectiveness of the FQNGD algorithm for the QFL in terms of a faster convergence rate on the training dataset and higher accuracy on the test one.

In this paper, we propose and analyse algorithms for zeroth-order optimisation of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional structure of the decision set using the stochastic mirror descent method with an entropy alike function, which performs gradient descent in the space equipped with the maximum norm. To improve the gradient estimation, we replace the classic Gaussian smoothing method with a sampling method based on the Rademacher distribution and show that the mini-batch method copes with the non-Euclidean geometry. To avoid tuning hyperparameters, we analyse the adaptive stepsizes for the general stochastic mirror descent and show that the adaptive version of the proposed algorithm converges without requiring prior knowledge about the problem.

We regularly consider answering counterfactual questions in practice, such as "Would people with diabetes take a turn for the better had they choose another medication?". Observational studies are growing in significance in answering such questions due to their widespread accumulation and comparatively easier acquisition than Randomized Control Trials (RCTs). Recently, some works have introduced representation learning and domain adaptation into counterfactual inference. However, most current works focus on the setting of binary treatments. None of them considers that different treatments' sample sizes are imbalanced, especially data examples in some treatment groups are relatively limited due to inherent user preference. In this paper, we design a new algorithmic framework for counterfactual inference, which brings an idea from Meta-learning for Estimating Individual Treatment Effects (MetaITE) to fill the above research gaps, especially considering multiple imbalanced treatments. Specifically, we regard data episodes among treatment groups in counterfactual inference as meta-learning tasks. We train a meta-learner from a set of source treatment groups with sufficient samples and update the model by gradient descent with limited samples in target treatment. Moreover, we introduce two complementary losses. One is the supervised loss on multiple source treatments. The other loss which aligns latent distributions among various treatment groups is proposed to reduce the discrepancy. We perform experiments on two real-world datasets to evaluate inference accuracy and generalization ability. Experimental results demonstrate that the model MetaITE matches/outperforms state-of-the-art methods.

Optimization on a Riemannian manifold naturally appears in various fields of applications, including principal component analysis [22, 61], matrix completion and factorization [35, 56, 13], dictionary learning [17, 27], optimal transport [49, 40, 26], to name a few. Riemannian optimization [2, 12] provides a universal and efficient framework for problem (1) that respects the intrinsic geometry of the constraint set. In addition, many non-convex problems turns out to be geodesic convex (a generalized notion of convexity) on the manifold, which yields better convergence guarantees for Riemannian optimization methods. One of the most fundamental solvers is the Riemannian gradient descent method [55, 62, 2, 12], which generalizes the classical gradient descent method in the Euclidean space with intrinsic updates on manifolds. There also exist various advanced algorithms for Riemannian optimization that include stochastic and variance reduced methods [11, 61, 34, 24, 25], adaptive gradient methods [8, 33] quasi-Newton methods [30, 43], trust region methods [1], and cubic regularized Newton methods [3], among others. Nevertheless, it remains unclear whether there exists a simple strategy to accelerate firstorder algorithms on Riemannian manifolds. Existing research on accelerated gradient methods focus primarily on generalizing Nesterov acceleration [42] to Riemannian manifolds, including [37, 4, 63, 6, 31, 36]. However, most of the algorithms are theoretic constructs and are usually less favourable in practice.

Gradient estimation is often necessary for fitting generative models with discrete latent variables, in contexts such as reinforcement learning and variational autoencoder (VAE) training. The DisARM estimator (Yin et al. 2020; Dong, Mnih, and Tucker 2020) achieves state of the art gradient variance for Bernoulli latent variable models in many contexts. However, DisARM and other estimators have potentially exploding variance near the boundary of the parameter space, where solutions tend to lie. To ameliorate this issue, we propose a new gradient estimator \textit{bitflip}-1 that has lower variance at the boundaries of the parameter space. As bitflip-1 has complementary properties to existing estimators, we introduce an aggregated estimator, \textit{unbiased gradient variance clipping} (UGC) that uses either a bitflip-1 or a DisARM gradient update for each coordinate. We theoretically prove that UGC has uniformly lower variance than DisARM. Empirically, we observe that UGC achieves the optimal value of the optimization objectives in toy experiments, discrete VAE training, and in a best subset selection problem.

Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular approaches to solving the minimization problem. Although existing methods can achieve implicit model identification, aka support set identification, in a finite number of iterations, these methods still suffer from huge computational costs and memory burdens in high-dimensional scenarios. The reason is that the support set identification in these methods is implicit and thus cannot explicitly identify the low-complexity structure in practice, namely, they cannot discard useless coefficients of the associated features to achieve algorithmic acceleration via dimension reduction. To address this challenge, we propose a novel accelerated doubly stochastic gradient descent (ADSGD) method for sparsity regularized loss minimization problems, which can reduce the number of block iterations by eliminating inactive coefficients during the optimization process and eventually achieve faster explicit model identification and improve the algorithm efficiency. Theoretically, we first prove that ADSGD can achieve a linear convergence rate and lower overall computational complexity. More importantly, we prove that ADSGD can achieve a linear rate of explicit model identification. Numerically, experimental results on benchmark datasets confirm the efficiency of our proposed method.